Two vibrating strings of same length, same cross-sectional area and stretched to same tension are made of material with densities \(\rho\) and \(2\rho\). Each string is fixed at both ends. If \(V_1\) and \(V_2\) are speeds of transverse waves in the strings with densities \(\rho\) and \(2\rho\) respectively, then \(\frac{V_1}{V_2}\) is: